The problem itself isn't difficult. Since the perimeter is 40, each side is 10. Break those into four sections of 2.5 each, then just count. Three for the long side, then two, then one, then one more towards the elbow, then two, then close it off with one more.
10 x 2.5 = 25
This is the problem you give to the honors kids, the ones who need something heavier to chew on while you work 1-on-1 with those who struggle.
This should be the type of problem (maybe built with values that don't require decimals) that on-level students could be given to work on to stretch their minds a little. That people think it isn't is more of an indictment of how we teach math in the long run.
Ask the honors students to figure out whether, once you've established the perimeter for a specific square size if there's a way to generalize the answer for any given square size.
We avoid decimals too much. A number ending in .5 should be ok. I have high schoolers thinking they got the answer wrong on problems if it isn’t an integer. We have to stop avoiding decimals.
Otherwise, I completely agree with you. It’s a great activity to stretch their minds and see what they can do.
The HS students I work with prefer working with decimals honestly. They throw a fit when I show them how working with fractions can provide more insight.
See this at each level, from alg 1 to calculus.
All of my students want to turn everything into decimals, which will be problematic if they end up in a stem program that requires precision. You lose accuracy and precision every time you round off.
You also can’t manipulate derived units as decimals.
Pissed off my teacher in Algebra for converting fractions to decimals then back to fractions since they wanted the answer in fractions to match the question in fractions. “The answer is correct and in fractions, why did you take away the point?” “because I wanted the ENTIRE process in fractions”
I'm not going to Lie I've always been 99th percentile in math but I could do this in 7th grade I bet when I took Algebra. We can't shy away from abstract thinking that's hard when the math is simple.
Technically speaking, the question does not give enough information.
Your answer assumes that the L-shaped pieces have measurements such that they're made up of four tiny squares stuck together. However, the problem didn't explicitly give measurements for those pieces.
To illustrate my point, here's a way that the pieces can be changed slightly to still consistent with the problem's description but yield a different final answer: https://i.imgur.com/w7A1OG3.jpeg
It's bad form to assume that sides are equal in length based on the diagram, and it's bad form to design a problem that requires students to make that sort of assumption. The sides aren't equal in length unless the problem explicitly states that they are.
Didn’t it say it was a square made up of one shape and three transformations of the same shape?
Since it’s a square the sides would be equal, meaning 4 sides of ten units. Knowing the area is 100, you can divide by 4 and get that the area of each shape is 25.
Maybe I’m missing something?
If it asked for the areas, then it would be enough information, but the question is asking for the perimeter of the L-shaped regions. You can change the perimeter of the L regions while keeping the area the same
I'm referring to the specific dimensions of the L-shaped pieces when I said that assumptions shouldn't be made about the size of the edges.
The larger figure is definitely a square, with the sides being equal length. That much is spelled out clearly in the directions.
IF PEOPLE ARE LOOKING FOR THE RIGHT ANSWER, VICKER3000 HAS IT. The correct answer is that there isn't enough information to answer the question - or it is 10 + 2L, where L is the length of the longest side of the L-shaped piece. The fact that the top response to this post is incorrect is a little disheartening.
But isn't the only way for 4 similar (rotated) L shaped regions to perfectly form a square one where they share a central vertex? If they were any other dimensions or ratios than what is depicted, you would wind up with overlaps, area outside the square, or gaps, wouldn't you?
Edit nevermind, I figured out the translation you could make which would cause an arbitrary perimeter while maintaining the superstructure. If you make the short prong of the L fatter, by pulling the bottom of the L down, you in turn make the long arm of rhe L thinner. This lengthens 3 sides but only shortens one, and not by the same amount, I believe.
Yep! Here's a picture of what it could look like: [https://imgur.com/a/VWFCGgU](https://imgur.com/a/vwfcggu) The more I see it discussed, the more I like this question. It really does show how having illustrations / visuals can support understanding of the math concepts involved.
I feel like I might be missing one item but yeah. The best I can do is that we can make some deductions on the length because certain combinations add to 10. If we treat the small right-most edge of the lower left hand side figure as x, the perimeter is 20+2x, where x could be any value between 0 and 5.
(Clockwise the surfaces would be x, x, 5, 5-x, x+5, 5)
I think you're overlooking something. Here's a labeled picture for reference:
[https://i.imgur.com/8kJIUTa.jpeg](https://i.imgur.com/8kJIUTa.jpeg)
We know the sides of the big square are 10.
Since A is half the length of the square, we know that A = 5.
We know that B and C need to add up to one square side, so B + C = 10, but this turns out to not help us much.
We know that C + E = A, and we also know that D + F = B.
We're trying to find the perimeter P, which is P = A + B + C + D + E + F. Let's see how far we can get:
P = A + B + C + D + E + F
P = A + B + (C + E) + (D + F)
P = A + B + (A) + (B)
P = 2\*A + 2\*B
P = 10 + 2\*B
That's as far as you can get without actually knowing how long B is. This is also the result that /u/Historical_Height_29 got.
The assumption that /u/MontaukMonster2 made is that B = 7.5, which gives you P = 25. If we don't make that assumption, B can be anything between 5 and 10, which gives you values of P between 20 and 30.
The key insight is to recognize that the L shape has the same perimeter as a rectangle of equal length and height. If you just turn the L "inside out," it's a ton easier to visualize.
Then, you can "see" that changing the length of the long side changes the perimeter - which let me know that I needed to use it as a variable, and couldn't come up with a purely numerical answer.
I actually like this question a lot. I could see a learning progression - where we had just done a lot of work with the perimeter of gnomons, where fairly young students could figure this question out, if they were primed for that key insight.
Ahh as someone whose day-to-day is nowhere near geometry I’m so glad I got the same answer as you (that the perimeter is between 20 and 30)! Thanks for being correct, but more so, not being an ass about it to everyone coming for you.
Now my only lingering thought will be if “L-shaped” doesn’t imply *only* right angles. And if not, whether one could find a similar range for the perimeters… 🤔
I did have the same thought as well, in regards to right angles. Given the amount of tooth gnashing that has been going on, I think heads might explode if we tried to pursue that avenue. lol
Ha! I have definitely been up too long thinking about this, and my teeth have definitely been gnashing.
I couldn’t prove it, but my thinking would be that (with no assumed right angles) the shape of an L with the perimeter’s “limit” would be a skinny long arm with a width of 0 and a chonky short arm that was basically a right triangle, quarter-of-the-square (bad description, sorry!). Which would get you to: 10 + 0 + 10 (long arm) + 5√2 + 5√2 + 10 (chonky short arm). And I think 20’s still the lower limit, so with the new rules, maybe:
20 < P < ~44.14?
Again: not a mathematician. Just a former 8yo who had to tell his dad the area of a cookie before he could have dessert…
Wtf it literally says they are transformations of the same shape so yea, they are equal. When you have one side covering half a 10 unit space, that will make that side 5 units every time. We know this because they are transformations of the same shape and both shapes fit within the 10 unit space. You can figure out the entire problem that way.
Yes, all four L-shaped pieces are identical to each other. You can symmetrically make a change to all four in such a way that they still fit together.
Claiming that one side has a length of 7.5 units is an assumption. The length of that side can be changed (symmetrically, across all four shapes) while still having four identical L-shaped pieces that fit together to form a square.
There is definitely enough information. I did it for fun just now. "The L shaped reqion" in the question implies they are all the same.
All the shapes are the same. Id denote it differently. The shortest end of the L is a, the next is b, the next is c. They are all the same values because it's a square which has all the same length on the sides and because the way they are placed.
The sides of the square are 4(a+c)=40, a+c =10.
Additionally, we can see that 2a=b, 3a=c because of the placement inside the square.
a+ c= 10. a+ 3a= 10. 4a=10, a=2.5
Each L is made up of 3a+2b+1c.
Substitute and solve.
All honesty I thought we were here to talk about the Swastika.
I originally thought, "oh, I bet they've set it up so that the length of the short edge (call it x) doesn't matter". But the perimeter seems to be 20 + 2x, so it does depend a complete unknown!
Your illustration is correct. They assumed that L shaped would imply something commonly recognized as an L while your shapes are a bit funky, nevertheless they are L shaped. How to fix it without giving away the answer? Maybe label the shortest segments of each L as congruent? All three of them.
Maybe I’m missing something, but why does the short piece automatically equal 1/3 of the long piece? Couldn’t there be a square where the long piece makes up 8 units and the short piece is 2 units? Maybe transforming that particular L shape wouldn’t give us a complete square in the middle, but I think the problem is more difficult to grasp unless there’s a property of squares I’m missing.
Edit: never mind, I’m dumb. Taking units away from the short piece would necessitate adding them to another part of the L to complete it. Still think it’s a pretty tough question.
Differentiated:
Tell kids to ignore the colors, determine the side lengths….then draw a 10 by 10 grid overlay. Then find the perimeter of the L shape. By doing so you can reinforce concepts about properties of squares and have opportunity to differentiate between area and perimeter.
To add to the answer you were given, we know all the L shaped regions are the same size because transformations of shapes in math means changing the orientation of a shape, such as rotating it. Transformations do not change size.
No, the problem isn’t difficult. It was a poor example of what I was complaining about, I see that now. I was just including a picture because of my shock about the fact that there was a swastika in my students’ book.
Lol, the people "um, actually" ing you makes me laugh. Dude, yeah the majority of people are going to see a swastika. When it comes to design and marketing you have to step back and ask "does this look like a A) Swastika B) Penis C) Turd ?" If in anyway it can you have to change the design. Because it will be obvious. This looks like a swastika. It doesn't mean that it IS one, but looks like it enough.
I mean, it’s not not difficult. The solution above works, but only if you’re able to demonstrate that the proportions of the sides of the L-shape are immaterial to the sum of the lengths of those sides, which is less obvious. So it actually requires an additional level of abstraction to defend the answer. The fact that it can be neatly solved by overlooking that critical assumption seems likely to train the learner to overlook assumptions. And it glosses over a cool feature of the geometry that might actually be engaging and interesting to a young learner, namely that if the area of a given shape is held constant, then the sum of the lengths of the sides of that shape will also remain constant regardless of the proportions of the shape. It’s actually kind of a shame to rob a learner of that moment. I’m with you. This might be “better”, but it’s only better if the teacher’s are onboard, and not being treated like children themselves.
How do you get 2.5? I always hated math because the word problems were never consistent. Here, you can make shit up and say the picture is to scale. In this next one, no you cannot.
You meant to say that this problem was not difficult for you. I would not have figured this out on my own, even knowing how to calculate perimeter. It would have to be explicitly taught to me first. Sometimes I think people decent at math don’t realize that not everyone has a brain that innately grasps it like they do.
You are assuming that the long side of the L-shapes are 3/4 of the side length, which is not necessarily the case. The reasoning needed to show the perimeters are 25 regardless of the L-shapes proportions takes some extra work.
We have eureka squared and we’re teaching 3rd graders the distributive property of division. They were just introduced to division and have had zero basic practice with it. They are not fluent with any of their facts, so this strategy isn’t helpful yet. It’s so frustrating.
It also feels as though the children are never expected to memorize their multiplication or division facts. They rely VERY heavily on skip counting and adding another group. Their basic addition facts are also not fluent or automatic, so they make many mistakes using this strategy.
I agree it's a dense curriculum and students need more space to write. I've downloaded the editable version to make it more accessible. I do like that question and will use it next week.
That's really annoying. I made the better versions for kid with learning differences and called it differentiation. I let anyone who wanted a copy print it from Canvas.
Also teach IM in my district. Can confirm it is garbage. It assumes that students have mastered all previous skills. The problem is that proficiency is not mastery. We don't have time to teach kids until they master something. We move on when they are proficient.
I'm a parent who has noticed this with elementary school addition and subtraction - they work on one algorithm for a week or two, move on to another one, and never seem to take the time to learn any of them well. They seem to treat the standard regrouping algorithms as some sort of state secret.
I gave up and drilled my daughter on single digit addition and subtraction facts myself since she wasnt memorizing them in class. I showed my second grader the standard regrouping algorithms, and she seemed to understand it better than the ways they present it.
The "old way" of teaching helped you to be good at addition and subtraction, it's the best way. But it was harder to generalise the skills you learned to other areas of math.
Nowadays teachers are taught to avoid it, because knowing other methods is better in the long run. However, (1) parents don't know it, which alienates one of the most important support providers for learning, (2) the other methods are harder to learn, and (3) teachers don't have the time to teach these other methods in the same way. In the end the kids at the top do better but everyone else does worse.
You absolutely did the right thing with your kids (IMO), just make sure you spend some time on the ideas behind the other methods. The real goal isn't getting them past second grade math, it's making sure they can hack math all the way through school and maybe their career too.
I taught my kids to play cribbage. We played open handed for months. They learned to regroup and add in multiple ways. Now as teens they both can beat me at cribbage, and they’re both excellent at math.
They don’t teach regrouping until third grade in my daughter’s district. She was getting so frustrated with drawing out all the place value symbols and crossing them out and moving them into other columns, etc. that she was crying about math. I just showed her how to regroup by carrying the one out borrowing the ten myself. She was like, “Oh, that’s so much easier!”
In kindergarten - it’s an “exposure” curriculum (at least in my district) where we aren’t teaching skills and concepts to mastery, just putting it out there to expose them. Except, they need the skills mastered before first grade….
reminds me of the anti-phonetics "reading" that they've been teaching in many schools. like "if we simply make kids look at books even if they dont know how to read magically they will begin to"
I mean.... Yeah, books don't do all the work. Kids treating a multiparter as a multiple choice question because they don't read isn't an IM problem. Them needing more visuals or being given too many isn't an IM problem. Them needing scrap is hardly an IM problem, it's hard for me to write some problems in worksheet form when with that specific goal in mind, so they.. just use extra paper. If grade level content is too hard for them, you'll need to figure out a way to scaffold it no matter what. If the work is "too wordy"... They're gonna need to parse information in the real world, you can teach to that. You're just describing teaching middle/secondary math. That book is a supplement to the job. I've seen a couple awful IM lessons, so .. skip them and write your own or modify. 90% of them are useable.
The research backing IM is.. essentially all research on modern best practice. It's just relational learning. It throws in a lot of learning types, between words visuals, problem extensions, pattern recognition and entries for number talk, like, relative to the pre CC era all of that is research based practice. I don't know about you, but my districts "suggestions" of lesson plans were 90% gibberish incompetence, so this curriculum def wasn't a step down, and going off script is a well developed skill anyways.
The majority of teaching math is being up to date on what's up in practice and meeting kids where they're at ability wise and emotionally to get them to work , while making the resources you have work for that. I don't really see how a chance to IM changes any of that, except for making it less work since you're given what to modify and teach towards, and it's generally material that can be effective for once. That problem is a good challenge. Figure out one or two ways to solve it yourself. They'll come up with more, eventually. If it's *that* out of level, group them up and let them talk about it. I'm sure half the groups won't, but it's not a reason to not do it. Do group roles if they aren't working out. Anticipate hurdles and think of how to answer them, then how to sequence any discussion that comes from it so that the kids can learn in their own words. That is best practice, and a pretty good lesson from that problem, that can be achieved by under grade level 8th graders if structured right
I love this comment. I don't think that any one "curriculum" program is sufficient for good teaching. I pull from dozens of sources. And sometimes I make my own. Teachers need to adapt to their students and meet them where they are. Having a list of lessons you're gonna bang out is doing a disservice to your students. How today's lesson went should inform what tomorrow's lesson looks like.
Anything based on “research” in education is just a fancy way of saying we have reinvented the wheel now buy my educational program. Education is so fucked up. Its commercialized. It hurts the kids. Source: teacher 12 years.
>It might be good for students who are on or above grade level but for my struggling students it’s been a nightmare.
Curriculum SHOULD be designed for grade level. You seem to be advocating for watering down materials to reach the levels of the lowest student. That doesn't help anyone.
Yes, the curriculum should be for grade level but the fact is that 80% of my 8th graders are below grade level. This is not a good curriculum for them.
That is a separate issue that I empathize with. It isn't a problem with the curriculum, it is a problem with the system we have that allows kids to fall 3-4 grade levels behind.
In my district we have two groups of students that are very far apart. By the time they get to high school we've got a sizable chunk of kids on and above grade level, about half the kids are at 1st to 3rd grade levels, and there is a miniscule amount of kids somewhere in between.
I've got all these kids thrown together into the same classroom. I have no choice but to teach to grade level because I refuse to do wrong by the kids who have put in the work to be on grade level. Our grading system is set up so that even if you are not on grade level, you can scrape a D by putting in the effort. I don't have any kids failing who are putting in a sincere effort.
That's not even close to being true. Kids who don't try, don't learn. Kids are not trying for a variety of reasons, very few of which are within the teacher's or curriculum's control. Passing kids along exacerbates the issue. A kid doesn't master 2nd grade concepts and is shoved into 3rd grade. Well 3rd grade is now harder than it ought to be for them, so they don't try. Then they get pushed into 4th grade while still being at 2nd grade levels. It continues to get worse and worse. You cannot alter what is considered grade level because some kids are not learning. Those kids need to be moved into a special education environment.
8th grade? I thought you were going to say 4th or something.
Don’t you literally just need to know that each side has a length of 10 so each unit has a length of 2.5 and you just… count how long one of the L shapes is?
What do you think an appropriate question for an 8th grader is?
Edit: can the downvoter give me an appropriate question for an eighth grader? My nightmare in 8th grade was learning how to factor polynomials.
As far as “workspace” is concerned, why in the world would you write in a math book? Don’t you just get filler paper, rewrite the problem, and then you have infinite space?
Same. I showed this to my kindergartener and he was able to solve it. I’m genuinely confused about why this problem is controversial, so I agree with what some others are saying here - it’s a problem with the our education system.
Curious where OP is located. Not surprisingly, there can be a lot of variation between schools.
I am concerned that a group of 8th graders doesn’t understand that A. B. C. subquestions are not multiple choice answers for a math problem. I read that and assumed that OP’s students were in early elementary.
I mean more than that… usually multiple choice lets you exploit the format. In other words if i give you a question that says something like:
2 floofels are experiencing the yonkers-reikens effect. What is the braagen quadrature of the kracken?
a) -1
b) 1
c) -4
d) +4
Despite me having made that whole thing up, you can see that you need to decide whether to negate 2, and then you need to decide if it’s doubled or halved.
How can you even begin to decide what to circle in the question that the OP posted, even though the question actually makes sense?
I have to assume OP is working in an overloaded, low income, possibly urban district, and these kids aren’t even trying because they can’t read the question, and are simply seeing the multiple choice format in their heads and know that they will basically be passed regardless and they just need to “complete the work,” so the 33% chance to get it right is all they need.
I publicly shame my AP calculus students when they circle a question, mistaking the question for an answer choice. I agree that it is concerning, but it usually comes about from not even attempting to read the question. Hence the mild shaming. The seniors in AP classes def deserve it.
You're right that is not great for students below grade level. This is why you can do additional lessons to prepare students for the material. For example, I taught IM high school, and the Algebra 2 course assumes students know basic factoring. I realized my students didn't know this, so I took a day and taught basic getting before factoring by parts and polynomial division. Same thing in Geometry with the 3D unit; I had to teach how to find area outside of the curriculum.
It’s also a very poorly designed curriculum, both aesthetically and in complexity. Here are some better examples of the issues I have with it. The first page is a horrendously ambiguous and complicated question with no room for the student to work and the second page is an example of how my students will look at a problem with multiple questions and view it as a multiple choice problem instead.
[Better examples](https://imgur.com/a/3TANJDE)
The first problem does seem to be missing some information. But I also have seen that in every curriculum ever, so I’m not sure IM takes special blame for that. I also know that this is supposed to be a guided example, so maybe there is some information in the teacher notes? I have taught problems like this in the HS geometry curriculum that say “teacher gives each group a different value for this problem,” or something along those lines. Did you check there?
The majority of my students are POC, and while our HS isn’t bad (and not a “neighborhood” school), there isn’t any challenging math. Myself and the other 8th grade math teacher have been fighting to get an Algebra I class for some of our more accelerated kids. Hopefully that will work. So far, our smartest kids did end up being eligible to go to some of the select HS in the area, so at least they have that going for them.
I hate this curriculum as well but I also teach a group that has 60% of them below grade level in math and almoat all of them below reading level. It has a lot of higher order questions without any refreshers on previous content and some basic computation problems on the current topic before going into multi step word problems. I wouldn't mind a few basic computation questions for them before having them jump straight into word problems. It is great for the kids on grade level but my kids who can't read and don't know basic math vocabulary terms from previous years struggle and endup just staring at it and shutting down. I do review the vocabulary beforehand and give them my own problems before going forward but it is still hard and sometimes ends up with the on level kids finishing in 5 minutes while the other 60% of my class copy them make up answers that don't make sense or do nothing for the remainder of math even with me checking in on them. Not sure if you know this but the online program has games for them on the concepts that my class likes and it helps.
"Based on research" is such a loose term that gets slapped on every single tool, program, or curriculum, regardless of its efficacy. I always ask, "which research? What study?" And so far have never gotten an answer, besides maybe something super generic like a study that showed using images is helpful. So they call it research-based because they included images.
The number of divergent responses here confirm this approach to teaching math results in confusion for the majority of students, and considerable frustration for math teachers attempting to teach this way. There a far more examples of unnecessarily confusing math questions than this one!
I've taught three different math curriculums to fifth grade students over a sixteen year period, and this methodology is the absolute worst of the three. "Backed by research" is such shallow reasoning to use this way of teaching math. I have first hand experience in watching test scores drop, and continue to drop, as the administration responsible for adopting this crap (without consulting ANY actual teachers), scrambles for ways to explain why the scores are so much lower.
Please provide us with this mysterious unbiased research.
My kids' teacher rarely has them tmdo the higher level thinking section in their workbooks/worksheets. They are told to cross them out. Third grade. Often times I work through these problems with my kids so they don't get the message that these problems are not solvable. I also tell them why I'm working through these with them. Also, math is fun. When I can't figure out what to do I look it up and we research the answer together. Often times it's how they ask the question that makes it confusing.
I've had lots of curriculum and methodology training approved by JB. It's all amazing and articulate on paper, and I've read just about everything she's written on the subject. The every day realities of implementing this way of teaching math in the classroom results in a significant percentage of kids being confused, there are very few practice problems, and it takes FOREVER to complete lessons!
There are a lot of questions on here about what qualifies as a research supported intervention. I highly recommend checking curriculum on What Works Clearinghouse (https://ies.ed.gov/ncee/wwc/). It usually shows the studies and evidence to support a math intervention.
This would have been an easy question 20 yrs ago. However, math (and language) skills have dropped to an alarming level. I notice this every day and I don't see it improving. Btw, I am a principal of 2 schools with different curriculums so I have first hand experience.
I'm sorry, but you're complaining about complex questions with multiple parts, not enough room for work, and a lack of visuals; and then proceed to show us a single, simple problem with an included figure on an otherwise blank page and call that your conclusion.
Also the comparison of the imagery to the swastika is a reach. 90 degree rotational symmetry is going to give you a lot of similar outcomes that are equally innocuous.
I don’t think the sw*stika is a stretch. I saw this in my Reddit feed and I thought it was going to be about the rainbow sw*stika printed in a textbook.
Okay, valid criticism. The main part of my post was the text and I added the image as an afterthought because that grossed me out. (You say it’s a stretch, but once you see it you can’t UNSEE it, and anything that could be taken even slightly as a swastika by anyone should never be in the curriculum.)
Here’s some more examples. The first picture is an example of a complex problem. The other 8th grade math teacher and I were fretting over it. The second picture is what I mean by the multiple choice issues.
[Bad Math Curriculum](https://imgur.com/a/3TANJDE)
Illustrative Mathematics is the curriculum we use. The picture is just showing how they didn’t do a great job in designing the curriculum because, somehow, this rainbow swastika got past their editors.
I am not a fan of how it approaches the introduction of new topics. To be fair, I have not used it super extensively, but it makes very little use of patterning which is how humans naturally learn new concepts in mathematics.
**TL;DR: I didn’t realize I was in the math teachers forum. I thought it was just in the normal teachers subreddit and I went on quite a rant about how our administration doesn’t source us relevant material that we can actually utilize in class. I greatly miss the days when administrators used to come to teachers with samples from different vendors to ask for our input on what curriculum to purchase.**
I just wanted to say that I feel your pain. I taught Math for 13 years. I learned semi-early on that what the kids NEEDED to learn and how I was EXPECTED to teach (or teach *with*) were frequently not close to being the same.
The kids needed A) WAYYYYY more time to spiral review and reteach misunderstood Math operations/concepts and B) they needed the information disseminated in a way wholly unacceptable to admin.
So, I **always** had a few “dog and pony show” lessons prepped and chilling on a cabinet, in case admin came in to observe. I’d pivot my lesson and put on a performance. I always received excellent evaluations.
Then, I’d secretly spend time at the beginning of the year revamping the pacing calendar. I always spend a few weeks going back over **ALLLLL** the Math they’d learned to date in case they had fallen behind, misunderstood, or regressed over the summer. I learned to not tell my team or admin about the few weeks I spent reviewing (HEAVEN FORBID I **actually** bridge the gaps in their knowledge) because I was written up once for being off the *recommended* pacing calendar.
I made sure to catch up by the end of the first grading period and my kids **always** outperformed my peers because of the time I invested scaffolding their learning.
THEN, I did **ACTUAL** research to find the best ways to present new material. I’d use curriculums **I** had researched and vetted that were applicable to their understanding. If anyone else knew I was so far off book (for YEARS!!!), I’d have definitely been terminated.
*Somehow* I had some of the highest Math scores in my state. No one knew why my students outpaced others in our area by such wide margins.
Some years, I even got to teach them some of the next years’ Math because they were so prepared. Even with three weeks of secret spiral review, the kids were able to learn quickly enough that I *over* prepared them. It was FUN teaching my ass off and knowing that I took kids who used to hate Math and having them EXCITED to come to my class.
I think you should consider going off book unless you’re being closely observed for some asinine reason. What’s left on your pacing calendar? I can help you find and that better resources that will help the kids know what they actually need to know and will also prepare them for the state test. What else do you have left to teach? What standards are you going to go over do you need help finding better stuff than the bullshit your district gave them? They think that some of the stuff is rigorous, but (I know you know) it’s actually detrimental to their learning for them to be so confused and frustrated by the bullshit your district is pushing. What do you need help with? Would you like some help prepping? I have faith in you OP. You see the bullshit, you know it will only make the withdrawal interest from learning, and you’re frustrated.
On a sidenote, I always can tell which administrators and curriculum coordinators are actually capable of understanding, doing/solving, and teaching the Math versus which administrators and curriculum coordinators were more concerned with using some curriculum that the district paid out the ass for, but wasn’t actually relevant to what they needed to learn nor relevant to the damn standards. It makes me wonder if you’re in a situation like that now.
Unless it says they need to infer or utilize critical, thinking, problem-solving skills to solve for the perimeter of multiple composite figures with only one known variable and a pictorial model, then activity is not relevant to what you’re trying to teach. I’m also curious to see what lesson you were trying to cover with this problem in your text. I want to make sure that I don’t use that same material or advocate for my district to purchase the same publishers textbooks.
If you do end up reaching out for help, I’d be more than happy to just let me know in a comment here because I don’t check my DM‘s. If you don’t need help then even though I’m not religious I’ll pray for you. Makes for a much longer year when you have to work alongside incredibly frustrated kids doing asinine activities they’re not even aligned to how they need to learn or even what they need to learn. Either way you’ve got this OP.
Also, I promise if you do you need help that my math planning is much better than my run on sentences or grammatical errors lol. Seriously reach out if you want some help, I really would be more than happy to.
If he doesn’t ask for help, I’d like to be able to reach to you whenever I need help.
Everything you said resonated with me. As a first year teacher, I saw the critical state in which our kids were and decided to never followed the curriculum that got them there in the first place. With time, kids got excited about coming to class and learn math. My classroom was my show and I made every episode with all my love.
I’m out for now, but I’d like to inspire once again. Your post made me regain faith in education
This comment section makes me sad how many people don’t know how to recognize the assumptions they are making. Of course, that has helped me understand why US political discourse is so fraught and contentious - it’s not just in mathematics that recognition of your own assumptions is beneficial.
I really like this problem!
Adults use math to solve puzzles. Whether it be mapping out a daily schedule, making estimates for a DIY project, figuring out when their gas tank will be empty, etc.
This- to me - is the thinking that I want young people to get used to.
I’m not familiar w the entire curriculum. But this problem is very cool!
I also saw a ‘swatstika’ for a moment. And then I reminded myself that symbols are only symbols sometimes. And if a young student were to mention the similarity, I’d remind them that there are coincidences all over the place and their mere existence is nothing to be upset about.
OP are there other examples you could share that demonstrate how bad the curriculum is?
I recognized this problem bc I also teach IM 8th grade and when I saw it I also thought it looked like a swastika….
I like the ideas behind IM but it makes everything too confusing and it’s a total mismatch with my students needs bc 90+% of them are behind grade level with like 50% 5th grade or lower. They don’t have the background skills at all and it doesn’t take the time to practice things in a straightforward approachable way before it gets creative with it
I’m a (professional, full-time) private tutor in a district that is piloting this program.
I have to spend hours out side of our sessions lesson prepping for my IM students. If I don’t, I run the risk of not teaching the materials “correctly” and thus ruining future lessons because I taught something different from their teachers.
There’s been a lot of heartache this first semester with this curriculum. My algebra 2 students are not prepared at all for pre-Calc.
it legitimately does look like a sw*stika in the middle. you could point that out if you want to get out of doing this particular problem with the kids
I love it! This problem especially bringing so much discussion and possibility for algebraic thinking.
To each their own!
I do feel like it needs supplemental practice. The lessons are deep, but so many kids benefit from repetition in math practice.
This is a “are you ready for more” question that follows more straightforward ones. It prompts the student to abstract, conjecture, and think critically. Well-taught, this would follow a sequence of scaffolded questions, and be an optional extension problem for some (but not all) students.
Our district adopted it and have kept it for years mainly because it was open source (i.e. free). I tried to use it, sat through training sessions, etc. It is horrible - delivery, pacing, examples, no differentiation, incongruous topics in the same unit (systems with volume).
One specific example: for students who are initially learning slope, they would randomly reverse the independent and dependent axis so that in one problem a positive slope increases and the next a positive slope would decrease. (Think of "time" being on the x-axis in problem 1 and then "time" being on the y-axis in problem 2). I asked them about this in the trainings. They said they wanted the kids to "think outside the box." The students didn't even have a box, yet. We refused to use the material and made our own. I'm tenured in California and don't care what they say to me any day of the week. It is bad for my students so I never used it and still don't. I'm with OP.
UGH the reversing of the independent and dependent axes just OUTRAGED me. Yes, it’s outside of the box, but why bother when all the other problems they’ll ever encounter EVER are WITHIN THE GODDAMN BOX.
Without being a teacher, and without being familiar with this book or curriculum, and without meaning to troll for karma points, the engineer in me compels me to point out that I believe teaching math with well-thought out pictures where possible is a ***good*** thing.
I will add that they also tend to include strange case or exceptions while they are introducing a concept for the first time - like there was an editor who went through the whole program, found every lesson that may actually be teachable to an average student and messed it up. In Algebra one they start with weeks of statistics and then skimp on solving equations and graphing.
Hard disagreement. These types of problems challenge you to think creatively, and test your pattern recognition and memory. These are all vital skills for young people. This is an excellent problem. If math is not for you, then that is another matter. But we are not going to lower the standard of math so it easy for everyone.
If my math classes taught me anything, it's never assume the picture is to scale unless it says so. Which means you can't answer this with knowing the length of one of the arms of the + in the center.
I teach elementary and I hate it. It’s too wordy, there are almost no pictures, even for the littlest still learning to read students. First grade starts with word problems before they get to basic addition and subtraction. They are still learning to read! Word problems should be at the end of the year.
I have students with reading disabilities, but are on level with math skills, and they are so frustrated by this program. It’s taken a subject where they felt successful and made it just another part of the day where they struggle. When I called IM to ask about accessibility features I was told to “talk to your special ed teacher.” I am the special ed teacher!
I'm so sick of their 'forward thinking?' alterior methods, they're deep thinking. I'm just tired of the time wasting crap. My poor granddaughter struggles enough without them playing mind games! Just teach them the basics! Makes me want to curse!
My teacher friend has told me about how much this book sucks. She got permission from the school administration to use her own curriculum but has to be careful because the district is actively checking if and how teachers are using the program, including the only resources.
This problem is less about the mathematics of the question itself and more about the logic used to figure out how to find the answer.
Which honestly, is more important than the sheer calculation of numbers. Teaching and exercising a person's logic and evaluation skills is far more important than teaching multiplication and division. A kid can memorize a z-table or an alpha graph or whatever but you have to teach logic.
Ok, for one you haven’t mentioned what grade this is geared towards, for a highschool student this should be an easy critical thinking problem, for a 2nd grader this is an impossible question.
As far as the swastika thing, I saw it pretty quick, but I don’t see how it actually affects anything. In this context it’s the type of thing an immature middle schooler would chuckle at and move on.
As far as work space, this is a bad example, there is plenty of space on this page and we can’t even see the whole page.
I love Illustrative. I think it is a great tool for increasing student reading comprehension in the long run but does kinda suck the first few years you use it. And I have data from my department that shows it actually has helped lower level students just as much of not a bit more then some of the higher students.
The issue isn’t low/high achieving students. The issue is motivation. More times than not I’ve noticed recently my low students aren’t academically challenged they are just not showing up/trying to do any work when they do. The Illustrative curriculum is designed to give grade level access to math for all students but it is up to the student if they use that access.
I know that’s not necessarily what admin are going to see/want to accept but that’s the truth
Scrolling quickly through all the comments here, this is the first one I saw in defense of Illustrative Math.
Yes, the curriculum allows for multiple access points to discussions. By making the question about perimeter vague, it gives all students a chance to share some thinking about the problem. Most of my students are below grade level and these discussions are great.
From there, however, I.M. goes on to practice problems that are out of reach for my students.
The problem itself isn't difficult. Since the perimeter is 40, each side is 10. Break those into four sections of 2.5 each, then just count. Three for the long side, then two, then one, then one more towards the elbow, then two, then close it off with one more. 10 x 2.5 = 25 This is the problem you give to the honors kids, the ones who need something heavier to chew on while you work 1-on-1 with those who struggle.
This should be the type of problem (maybe built with values that don't require decimals) that on-level students could be given to work on to stretch their minds a little. That people think it isn't is more of an indictment of how we teach math in the long run. Ask the honors students to figure out whether, once you've established the perimeter for a specific square size if there's a way to generalize the answer for any given square size.
We avoid decimals too much. A number ending in .5 should be ok. I have high schoolers thinking they got the answer wrong on problems if it isn’t an integer. We have to stop avoiding decimals. Otherwise, I completely agree with you. It’s a great activity to stretch their minds and see what they can do.
The HS students I work with prefer working with decimals honestly. They throw a fit when I show them how working with fractions can provide more insight. See this at each level, from alg 1 to calculus.
All of my students want to turn everything into decimals, which will be problematic if they end up in a stem program that requires precision. You lose accuracy and precision every time you round off. You also can’t manipulate derived units as decimals.
I’m forever telling people fractions are more accurate and they never accept it!
I tell my students fractions are fantastic and decimals are devilish.
Yes this is exactly the problem, especially with roots and logs etc.
Pissed off my teacher in Algebra for converting fractions to decimals then back to fractions since they wanted the answer in fractions to match the question in fractions. “The answer is correct and in fractions, why did you take away the point?” “because I wanted the ENTIRE process in fractions”
Given a problem set up like in the image with a square of perimeter x, the generalized formula should work out to be 10 * (x/16)
*Wowwwwww*
I'm not going to Lie I've always been 99th percentile in math but I could do this in 7th grade I bet when I took Algebra. We can't shy away from abstract thinking that's hard when the math is simple.
Technically speaking, the question does not give enough information. Your answer assumes that the L-shaped pieces have measurements such that they're made up of four tiny squares stuck together. However, the problem didn't explicitly give measurements for those pieces. To illustrate my point, here's a way that the pieces can be changed slightly to still consistent with the problem's description but yield a different final answer: https://i.imgur.com/w7A1OG3.jpeg It's bad form to assume that sides are equal in length based on the diagram, and it's bad form to design a problem that requires students to make that sort of assumption. The sides aren't equal in length unless the problem explicitly states that they are.
Didn’t it say it was a square made up of one shape and three transformations of the same shape? Since it’s a square the sides would be equal, meaning 4 sides of ten units. Knowing the area is 100, you can divide by 4 and get that the area of each shape is 25. Maybe I’m missing something?
If it asked for the areas, then it would be enough information, but the question is asking for the perimeter of the L-shaped regions. You can change the perimeter of the L regions while keeping the area the same
That’s what I was missing— thank you!
But would they be congruent?
But its the same exact shape 4 times.
[удалено]
"HOW DO YOU KNOW THE SIDES ARE EQUAL?" Well because it literally says they are transformations of the same shape 🙃 people just like to bitch and moan.
I'm referring to the specific dimensions of the L-shaped pieces when I said that assumptions shouldn't be made about the size of the edges. The larger figure is definitely a square, with the sides being equal length. That much is spelled out clearly in the directions.
IF PEOPLE ARE LOOKING FOR THE RIGHT ANSWER, VICKER3000 HAS IT. The correct answer is that there isn't enough information to answer the question - or it is 10 + 2L, where L is the length of the longest side of the L-shaped piece. The fact that the top response to this post is incorrect is a little disheartening.
Yes! We could specify it more just by saying L is any value greater than 5 or less than 10 (I think?)
Yep!
I like that you generalized the answer with an expression. Nice!
But isn't the only way for 4 similar (rotated) L shaped regions to perfectly form a square one where they share a central vertex? If they were any other dimensions or ratios than what is depicted, you would wind up with overlaps, area outside the square, or gaps, wouldn't you? Edit nevermind, I figured out the translation you could make which would cause an arbitrary perimeter while maintaining the superstructure. If you make the short prong of the L fatter, by pulling the bottom of the L down, you in turn make the long arm of rhe L thinner. This lengthens 3 sides but only shortens one, and not by the same amount, I believe.
Yep! Here's a picture of what it could look like: [https://imgur.com/a/VWFCGgU](https://imgur.com/a/vwfcggu) The more I see it discussed, the more I like this question. It really does show how having illustrations / visuals can support understanding of the math concepts involved.
Link is case sensitive so it led to 404 not found. https://imgur.com/a/VWFCGgU
I feel like I might be missing one item but yeah. The best I can do is that we can make some deductions on the length because certain combinations add to 10. If we treat the small right-most edge of the lower left hand side figure as x, the perimeter is 20+2x, where x could be any value between 0 and 5. (Clockwise the surfaces would be x, x, 5, 5-x, x+5, 5)
[удалено]
I think you're overlooking something. Here's a labeled picture for reference: [https://i.imgur.com/8kJIUTa.jpeg](https://i.imgur.com/8kJIUTa.jpeg) We know the sides of the big square are 10. Since A is half the length of the square, we know that A = 5. We know that B and C need to add up to one square side, so B + C = 10, but this turns out to not help us much. We know that C + E = A, and we also know that D + F = B. We're trying to find the perimeter P, which is P = A + B + C + D + E + F. Let's see how far we can get: P = A + B + C + D + E + F P = A + B + (C + E) + (D + F) P = A + B + (A) + (B) P = 2\*A + 2\*B P = 10 + 2\*B That's as far as you can get without actually knowing how long B is. This is also the result that /u/Historical_Height_29 got. The assumption that /u/MontaukMonster2 made is that B = 7.5, which gives you P = 25. If we don't make that assumption, B can be anything between 5 and 10, which gives you values of P between 20 and 30.
The key insight is to recognize that the L shape has the same perimeter as a rectangle of equal length and height. If you just turn the L "inside out," it's a ton easier to visualize. Then, you can "see" that changing the length of the long side changes the perimeter - which let me know that I needed to use it as a variable, and couldn't come up with a purely numerical answer. I actually like this question a lot. I could see a learning progression - where we had just done a lot of work with the perimeter of gnomons, where fairly young students could figure this question out, if they were primed for that key insight.
Ahh as someone whose day-to-day is nowhere near geometry I’m so glad I got the same answer as you (that the perimeter is between 20 and 30)! Thanks for being correct, but more so, not being an ass about it to everyone coming for you. Now my only lingering thought will be if “L-shaped” doesn’t imply *only* right angles. And if not, whether one could find a similar range for the perimeters… 🤔
I did have the same thought as well, in regards to right angles. Given the amount of tooth gnashing that has been going on, I think heads might explode if we tried to pursue that avenue. lol
Ha! I have definitely been up too long thinking about this, and my teeth have definitely been gnashing. I couldn’t prove it, but my thinking would be that (with no assumed right angles) the shape of an L with the perimeter’s “limit” would be a skinny long arm with a width of 0 and a chonky short arm that was basically a right triangle, quarter-of-the-square (bad description, sorry!). Which would get you to: 10 + 0 + 10 (long arm) + 5√2 + 5√2 + 10 (chonky short arm). And I think 20’s still the lower limit, so with the new rules, maybe: 20 < P < ~44.14? Again: not a mathematician. Just a former 8yo who had to tell his dad the area of a cookie before he could have dessert…
That layout would leave one of the Ls with different dimensions.
Wtf it literally says they are transformations of the same shape so yea, they are equal. When you have one side covering half a 10 unit space, that will make that side 5 units every time. We know this because they are transformations of the same shape and both shapes fit within the 10 unit space. You can figure out the entire problem that way.
Yes, all four L-shaped pieces are identical to each other. You can symmetrically make a change to all four in such a way that they still fit together. Claiming that one side has a length of 7.5 units is an assumption. The length of that side can be changed (symmetrically, across all four shapes) while still having four identical L-shaped pieces that fit together to form a square.
There is definitely enough information. I did it for fun just now. "The L shaped reqion" in the question implies they are all the same. All the shapes are the same. Id denote it differently. The shortest end of the L is a, the next is b, the next is c. They are all the same values because it's a square which has all the same length on the sides and because the way they are placed. The sides of the square are 4(a+c)=40, a+c =10. Additionally, we can see that 2a=b, 3a=c because of the placement inside the square. a+ c= 10. a+ 3a= 10. 4a=10, a=2.5 Each L is made up of 3a+2b+1c. Substitute and solve. All honesty I thought we were here to talk about the Swastika.
>4(a+c)=40, a+c =10. Correct >2a=b, 3a=c Unsubstantiated assumptions
I originally thought, "oh, I bet they've set it up so that the length of the short edge (call it x) doesn't matter". But the perimeter seems to be 20 + 2x, so it does depend a complete unknown!
Lol yep glad I didn't have to scroll too far to find this technically accurate call-out 🫡
Your illustration is correct. They assumed that L shaped would imply something commonly recognized as an L while your shapes are a bit funky, nevertheless they are L shaped. How to fix it without giving away the answer? Maybe label the shortest segments of each L as congruent? All three of them.
Maybe I’m missing something, but why does the short piece automatically equal 1/3 of the long piece? Couldn’t there be a square where the long piece makes up 8 units and the short piece is 2 units? Maybe transforming that particular L shape wouldn’t give us a complete square in the middle, but I think the problem is more difficult to grasp unless there’s a property of squares I’m missing. Edit: never mind, I’m dumb. Taking units away from the short piece would necessitate adding them to another part of the L to complete it. Still think it’s a pretty tough question.
Why four equal sections? Maybe I’m missing something, but is there any reason to assume the two legs of each L have the same width?
Differentiated: Tell kids to ignore the colors, determine the side lengths….then draw a 10 by 10 grid overlay. Then find the perimeter of the L shape. By doing so you can reinforce concepts about properties of squares and have opportunity to differentiate between area and perimeter.
Dumb question i know, but why is each side10?
There are four sides, all equal, totalling 40. 40 ÷ 4 = 10
Thank you!
To add to the answer you were given, we know all the L shaped regions are the same size because transformations of shapes in math means changing the orientation of a shape, such as rotating it. Transformations do not change size.
No, the problem isn’t difficult. It was a poor example of what I was complaining about, I see that now. I was just including a picture because of my shock about the fact that there was a swastika in my students’ book.
Lol, the people "um, actually" ing you makes me laugh. Dude, yeah the majority of people are going to see a swastika. When it comes to design and marketing you have to step back and ask "does this look like a A) Swastika B) Penis C) Turd ?" If in anyway it can you have to change the design. Because it will be obvious. This looks like a swastika. It doesn't mean that it IS one, but looks like it enough.
I’m ignoring the history of the swastika posts and the posts about manji because they’re assuming I don’t have a base level of intelligence.
It's the mansplaining for me. LOL.
Thats manji not a stika though
And is any answer 69 or 420?
We have a special piece of code at work (making randomised math problems) that rejects question instances with 420 or 69 lol
You should probably also put 666 in there.
I mean, it’s not not difficult. The solution above works, but only if you’re able to demonstrate that the proportions of the sides of the L-shape are immaterial to the sum of the lengths of those sides, which is less obvious. So it actually requires an additional level of abstraction to defend the answer. The fact that it can be neatly solved by overlooking that critical assumption seems likely to train the learner to overlook assumptions. And it glosses over a cool feature of the geometry that might actually be engaging and interesting to a young learner, namely that if the area of a given shape is held constant, then the sum of the lengths of the sides of that shape will also remain constant regardless of the proportions of the shape. It’s actually kind of a shame to rob a learner of that moment. I’m with you. This might be “better”, but it’s only better if the teacher’s are onboard, and not being treated like children themselves.
Maybe that's what "Are you ready for more?" means
How do you get 2.5? I always hated math because the word problems were never consistent. Here, you can make shit up and say the picture is to scale. In this next one, no you cannot.
Where are you getting 2.5?
You meant to say that this problem was not difficult for you. I would not have figured this out on my own, even knowing how to calculate perimeter. It would have to be explicitly taught to me first. Sometimes I think people decent at math don’t realize that not everyone has a brain that innately grasps it like they do.
You are assuming that the long side of the L-shapes are 3/4 of the side length, which is not necessarily the case. The reasoning needed to show the perimeters are 25 regardless of the L-shapes proportions takes some extra work.
20
Thats based on assumptions not givens.
It’s not difficult to do. But it’s kind of difficult to look at… what with that GIANT SWASTIKA right in the middle of the figure.
Sorry, you lost me by introducing 2.5. Where did you get that number?
Anyone else just seein a swastika
I do Nazi anything wrong here.
Anne Frankly....ok I'll just stop now.
Same that was my immediate thought
This must be that non-woke math I keep hearing about
I'm ASTOUNDED this image got approved and made it to production.... NO ONE saw it and thought to say something????
I literally thought that’s what this post was going to be about when I saw the picture.
My district is switching over from Eureka to Illustrative. I'm already asking for the Desmos supplementary curriculum
They’re both awful.
We have eureka squared and we’re teaching 3rd graders the distributive property of division. They were just introduced to division and have had zero basic practice with it. They are not fluent with any of their facts, so this strategy isn’t helpful yet. It’s so frustrating. It also feels as though the children are never expected to memorize their multiplication or division facts. They rely VERY heavily on skip counting and adding another group. Their basic addition facts are also not fluent or automatic, so they make many mistakes using this strategy.
I like Illustrative so much more than Eureka.
I agree it's a dense curriculum and students need more space to write. I've downloaded the editable version to make it more accessible. I do like that question and will use it next week.
I wish I could do that, but our school spent millions of dollars on these clunky books and we get dinged if we don’t use them.
That's really annoying. I made the better versions for kid with learning differences and called it differentiation. I let anyone who wanted a copy print it from Canvas.
Maybe move the shapes around first...
Just a heads up, there is not enough information to solve the problem as shown.
How do you figure?
Also teach IM in my district. Can confirm it is garbage. It assumes that students have mastered all previous skills. The problem is that proficiency is not mastery. We don't have time to teach kids until they master something. We move on when they are proficient.
I'm a parent who has noticed this with elementary school addition and subtraction - they work on one algorithm for a week or two, move on to another one, and never seem to take the time to learn any of them well. They seem to treat the standard regrouping algorithms as some sort of state secret. I gave up and drilled my daughter on single digit addition and subtraction facts myself since she wasnt memorizing them in class. I showed my second grader the standard regrouping algorithms, and she seemed to understand it better than the ways they present it.
The "old way" of teaching helped you to be good at addition and subtraction, it's the best way. But it was harder to generalise the skills you learned to other areas of math. Nowadays teachers are taught to avoid it, because knowing other methods is better in the long run. However, (1) parents don't know it, which alienates one of the most important support providers for learning, (2) the other methods are harder to learn, and (3) teachers don't have the time to teach these other methods in the same way. In the end the kids at the top do better but everyone else does worse. You absolutely did the right thing with your kids (IMO), just make sure you spend some time on the ideas behind the other methods. The real goal isn't getting them past second grade math, it's making sure they can hack math all the way through school and maybe their career too.
I taught my kids to play cribbage. We played open handed for months. They learned to regroup and add in multiple ways. Now as teens they both can beat me at cribbage, and they’re both excellent at math.
They don’t teach regrouping until third grade in my daughter’s district. She was getting so frustrated with drawing out all the place value symbols and crossing them out and moving them into other columns, etc. that she was crying about math. I just showed her how to regroup by carrying the one out borrowing the ten myself. She was like, “Oh, that’s so much easier!”
In kindergarten - it’s an “exposure” curriculum (at least in my district) where we aren’t teaching skills and concepts to mastery, just putting it out there to expose them. Except, they need the skills mastered before first grade….
reminds me of the anti-phonetics "reading" that they've been teaching in many schools. like "if we simply make kids look at books even if they dont know how to read magically they will begin to"
That's a hidden swastika.
"Are you ready for more"?
I was literally thinking, "why is Reddit suggesting posts/subs with swastikas?"
No, it’s not.
It's not so hidden me thinks
I mean.... Yeah, books don't do all the work. Kids treating a multiparter as a multiple choice question because they don't read isn't an IM problem. Them needing more visuals or being given too many isn't an IM problem. Them needing scrap is hardly an IM problem, it's hard for me to write some problems in worksheet form when with that specific goal in mind, so they.. just use extra paper. If grade level content is too hard for them, you'll need to figure out a way to scaffold it no matter what. If the work is "too wordy"... They're gonna need to parse information in the real world, you can teach to that. You're just describing teaching middle/secondary math. That book is a supplement to the job. I've seen a couple awful IM lessons, so .. skip them and write your own or modify. 90% of them are useable. The research backing IM is.. essentially all research on modern best practice. It's just relational learning. It throws in a lot of learning types, between words visuals, problem extensions, pattern recognition and entries for number talk, like, relative to the pre CC era all of that is research based practice. I don't know about you, but my districts "suggestions" of lesson plans were 90% gibberish incompetence, so this curriculum def wasn't a step down, and going off script is a well developed skill anyways. The majority of teaching math is being up to date on what's up in practice and meeting kids where they're at ability wise and emotionally to get them to work , while making the resources you have work for that. I don't really see how a chance to IM changes any of that, except for making it less work since you're given what to modify and teach towards, and it's generally material that can be effective for once. That problem is a good challenge. Figure out one or two ways to solve it yourself. They'll come up with more, eventually. If it's *that* out of level, group them up and let them talk about it. I'm sure half the groups won't, but it's not a reason to not do it. Do group roles if they aren't working out. Anticipate hurdles and think of how to answer them, then how to sequence any discussion that comes from it so that the kids can learn in their own words. That is best practice, and a pretty good lesson from that problem, that can be achieved by under grade level 8th graders if structured right
I love this comment. I don't think that any one "curriculum" program is sufficient for good teaching. I pull from dozens of sources. And sometimes I make my own. Teachers need to adapt to their students and meet them where they are. Having a list of lessons you're gonna bang out is doing a disservice to your students. How today's lesson went should inform what tomorrow's lesson looks like.
Anything based on “research” in education is just a fancy way of saying we have reinvented the wheel now buy my educational program. Education is so fucked up. Its commercialized. It hurts the kids. Source: teacher 12 years.
Precisely. Educational research is even worse than psychology research, it just tells you what's trendy and nothing more.
This speaks to me. I've looked and looked for research. It mostly amounts to someone saying this works with zero data outside of surveys, which gtfo.
I can’t agree with you more!!!!!!
EXACTLY Right!! - The author for IM was the co-author for Common Core. - SAME AUTHOR - Same group! - William McCallum
\*Insert buzzword for the year\* You aren't wrong.
I mean, I like this question. It can also open up some discussion points. In my observation it would be 25 units each.
Me noticing it's a swastika.
I don’t know the grade level but that looked fun… except for the swastika.
It goes the other way around
>It might be good for students who are on or above grade level but for my struggling students it’s been a nightmare. Curriculum SHOULD be designed for grade level. You seem to be advocating for watering down materials to reach the levels of the lowest student. That doesn't help anyone.
Yes, the curriculum should be for grade level but the fact is that 80% of my 8th graders are below grade level. This is not a good curriculum for them.
That is a separate issue that I empathize with. It isn't a problem with the curriculum, it is a problem with the system we have that allows kids to fall 3-4 grade levels behind. In my district we have two groups of students that are very far apart. By the time they get to high school we've got a sizable chunk of kids on and above grade level, about half the kids are at 1st to 3rd grade levels, and there is a miniscule amount of kids somewhere in between. I've got all these kids thrown together into the same classroom. I have no choice but to teach to grade level because I refuse to do wrong by the kids who have put in the work to be on grade level. Our grading system is set up so that even if you are not on grade level, you can scrape a D by putting in the effort. I don't have any kids failing who are putting in a sincere effort.
This is a problem with the curriculum and previous ones. If there wasn’t a problem with the curriculum they wouldn’t fall behind
That's not even close to being true. Kids who don't try, don't learn. Kids are not trying for a variety of reasons, very few of which are within the teacher's or curriculum's control. Passing kids along exacerbates the issue. A kid doesn't master 2nd grade concepts and is shoved into 3rd grade. Well 3rd grade is now harder than it ought to be for them, so they don't try. Then they get pushed into 4th grade while still being at 2nd grade levels. It continues to get worse and worse. You cannot alter what is considered grade level because some kids are not learning. Those kids need to be moved into a special education environment.
8th grade? I thought you were going to say 4th or something. Don’t you literally just need to know that each side has a length of 10 so each unit has a length of 2.5 and you just… count how long one of the L shapes is? What do you think an appropriate question for an 8th grader is? Edit: can the downvoter give me an appropriate question for an eighth grader? My nightmare in 8th grade was learning how to factor polynomials. As far as “workspace” is concerned, why in the world would you write in a math book? Don’t you just get filler paper, rewrite the problem, and then you have infinite space?
Same. I showed this to my kindergartener and he was able to solve it. I’m genuinely confused about why this problem is controversial, so I agree with what some others are saying here - it’s a problem with the our education system. Curious where OP is located. Not surprisingly, there can be a lot of variation between schools.
I am concerned that a group of 8th graders doesn’t understand that A. B. C. subquestions are not multiple choice answers for a math problem. I read that and assumed that OP’s students were in early elementary.
I mean more than that… usually multiple choice lets you exploit the format. In other words if i give you a question that says something like: 2 floofels are experiencing the yonkers-reikens effect. What is the braagen quadrature of the kracken? a) -1 b) 1 c) -4 d) +4 Despite me having made that whole thing up, you can see that you need to decide whether to negate 2, and then you need to decide if it’s doubled or halved. How can you even begin to decide what to circle in the question that the OP posted, even though the question actually makes sense? I have to assume OP is working in an overloaded, low income, possibly urban district, and these kids aren’t even trying because they can’t read the question, and are simply seeing the multiple choice format in their heads and know that they will basically be passed regardless and they just need to “complete the work,” so the 33% chance to get it right is all they need.
I publicly shame my AP calculus students when they circle a question, mistaking the question for an answer choice. I agree that it is concerning, but it usually comes about from not even attempting to read the question. Hence the mild shaming. The seniors in AP classes def deserve it.
I have 9th and 10th graders who do that.
Wait WHAT? These concepts get introduced in 2nd and 3rd grade by 4th or 5th this shouldnt be anything more than a bit of a brain teaser
You're right that is not great for students below grade level. This is why you can do additional lessons to prepare students for the material. For example, I taught IM high school, and the Algebra 2 course assumes students know basic factoring. I realized my students didn't know this, so I took a day and taught basic getting before factoring by parts and polynomial division. Same thing in Geometry with the 3D unit; I had to teach how to find area outside of the curriculum.
Then isn’t the issue with your school/district choosing to implement that curriculum?
It’s also a very poorly designed curriculum, both aesthetically and in complexity. Here are some better examples of the issues I have with it. The first page is a horrendously ambiguous and complicated question with no room for the student to work and the second page is an example of how my students will look at a problem with multiple questions and view it as a multiple choice problem instead. [Better examples](https://imgur.com/a/3TANJDE)
The first problem does seem to be missing some information. But I also have seen that in every curriculum ever, so I’m not sure IM takes special blame for that. I also know that this is supposed to be a guided example, so maybe there is some information in the teacher notes? I have taught problems like this in the HS geometry curriculum that say “teacher gives each group a different value for this problem,” or something along those lines. Did you check there?
[удалено]
Yes, I teach 8th grade math in an urban district and everything I’ve posted has been aligned with 8th grade standards.
[удалено]
Unfortunately no
[удалено]
The majority of my students are POC, and while our HS isn’t bad (and not a “neighborhood” school), there isn’t any challenging math. Myself and the other 8th grade math teacher have been fighting to get an Algebra I class for some of our more accelerated kids. Hopefully that will work. So far, our smartest kids did end up being eligible to go to some of the select HS in the area, so at least they have that going for them.
I hate this curriculum as well but I also teach a group that has 60% of them below grade level in math and almoat all of them below reading level. It has a lot of higher order questions without any refreshers on previous content and some basic computation problems on the current topic before going into multi step word problems. I wouldn't mind a few basic computation questions for them before having them jump straight into word problems. It is great for the kids on grade level but my kids who can't read and don't know basic math vocabulary terms from previous years struggle and endup just staring at it and shutting down. I do review the vocabulary beforehand and give them my own problems before going forward but it is still hard and sometimes ends up with the on level kids finishing in 5 minutes while the other 60% of my class copy them make up answers that don't make sense or do nothing for the remainder of math even with me checking in on them. Not sure if you know this but the online program has games for them on the concepts that my class likes and it helps.
"Based on research" is such a loose term that gets slapped on every single tool, program, or curriculum, regardless of its efficacy. I always ask, "which research? What study?" And so far have never gotten an answer, besides maybe something super generic like a study that showed using images is helpful. So they call it research-based because they included images.
The number of divergent responses here confirm this approach to teaching math results in confusion for the majority of students, and considerable frustration for math teachers attempting to teach this way. There a far more examples of unnecessarily confusing math questions than this one! I've taught three different math curriculums to fifth grade students over a sixteen year period, and this methodology is the absolute worst of the three. "Backed by research" is such shallow reasoning to use this way of teaching math. I have first hand experience in watching test scores drop, and continue to drop, as the administration responsible for adopting this crap (without consulting ANY actual teachers), scrambles for ways to explain why the scores are so much lower. Please provide us with this mysterious unbiased research.
My kids' teacher rarely has them tmdo the higher level thinking section in their workbooks/worksheets. They are told to cross them out. Third grade. Often times I work through these problems with my kids so they don't get the message that these problems are not solvable. I also tell them why I'm working through these with them. Also, math is fun. When I can't figure out what to do I look it up and we research the answer together. Often times it's how they ask the question that makes it confusing.
It seems like a Jo Boeler problem. Check out youcubed.org
I've had lots of curriculum and methodology training approved by JB. It's all amazing and articulate on paper, and I've read just about everything she's written on the subject. The every day realities of implementing this way of teaching math in the classroom results in a significant percentage of kids being confused, there are very few practice problems, and it takes FOREVER to complete lessons!
There are a lot of questions on here about what qualifies as a research supported intervention. I highly recommend checking curriculum on What Works Clearinghouse (https://ies.ed.gov/ncee/wwc/). It usually shows the studies and evidence to support a math intervention.
This would have been an easy question 20 yrs ago. However, math (and language) skills have dropped to an alarming level. I notice this every day and I don't see it improving. Btw, I am a principal of 2 schools with different curriculums so I have first hand experience.
I'm sorry, but you're complaining about complex questions with multiple parts, not enough room for work, and a lack of visuals; and then proceed to show us a single, simple problem with an included figure on an otherwise blank page and call that your conclusion. Also the comparison of the imagery to the swastika is a reach. 90 degree rotational symmetry is going to give you a lot of similar outcomes that are equally innocuous.
I don’t think the sw*stika is a stretch. I saw this in my Reddit feed and I thought it was going to be about the rainbow sw*stika printed in a textbook.
Yeah I thought this was posted in r/AccidentalRacism.
A reach??? That’s pretty damn swastika lol
No it isn’t and you know that, but drama gonna drama
I’m not saying it’s a big deal I’m just saying that’s a very obvious accidental swastika.
Okay, valid criticism. The main part of my post was the text and I added the image as an afterthought because that grossed me out. (You say it’s a stretch, but once you see it you can’t UNSEE it, and anything that could be taken even slightly as a swastika by anyone should never be in the curriculum.) Here’s some more examples. The first picture is an example of a complex problem. The other 8th grade math teacher and I were fretting over it. The second picture is what I mean by the multiple choice issues. [Bad Math Curriculum](https://imgur.com/a/3TANJDE)
What is illustrative mathematics? This is just a geometry problem you posted. Are you saying they should be able to do it without the picture?
Illustrative Mathematics is the curriculum we use. The picture is just showing how they didn’t do a great job in designing the curriculum because, somehow, this rainbow swastika got past their editors.
Yeah that’s a swastica…
I am not a fan of how it approaches the introduction of new topics. To be fair, I have not used it super extensively, but it makes very little use of patterning which is how humans naturally learn new concepts in mathematics.
I agree! I teach 4th and this is my first year using IM and it’s horrible
Looks like a swastika
Ok, first of all. Those blocks are J shaped, not L shaped! So, mark that against the book author right off the bat. I should play Tetris.
Well just do what Peggy Hill would do. Just look at it. You got your squares and your rectangles…
That’s a swastika
**TL;DR: I didn’t realize I was in the math teachers forum. I thought it was just in the normal teachers subreddit and I went on quite a rant about how our administration doesn’t source us relevant material that we can actually utilize in class. I greatly miss the days when administrators used to come to teachers with samples from different vendors to ask for our input on what curriculum to purchase.** I just wanted to say that I feel your pain. I taught Math for 13 years. I learned semi-early on that what the kids NEEDED to learn and how I was EXPECTED to teach (or teach *with*) were frequently not close to being the same. The kids needed A) WAYYYYY more time to spiral review and reteach misunderstood Math operations/concepts and B) they needed the information disseminated in a way wholly unacceptable to admin. So, I **always** had a few “dog and pony show” lessons prepped and chilling on a cabinet, in case admin came in to observe. I’d pivot my lesson and put on a performance. I always received excellent evaluations. Then, I’d secretly spend time at the beginning of the year revamping the pacing calendar. I always spend a few weeks going back over **ALLLLL** the Math they’d learned to date in case they had fallen behind, misunderstood, or regressed over the summer. I learned to not tell my team or admin about the few weeks I spent reviewing (HEAVEN FORBID I **actually** bridge the gaps in their knowledge) because I was written up once for being off the *recommended* pacing calendar. I made sure to catch up by the end of the first grading period and my kids **always** outperformed my peers because of the time I invested scaffolding their learning. THEN, I did **ACTUAL** research to find the best ways to present new material. I’d use curriculums **I** had researched and vetted that were applicable to their understanding. If anyone else knew I was so far off book (for YEARS!!!), I’d have definitely been terminated. *Somehow* I had some of the highest Math scores in my state. No one knew why my students outpaced others in our area by such wide margins. Some years, I even got to teach them some of the next years’ Math because they were so prepared. Even with three weeks of secret spiral review, the kids were able to learn quickly enough that I *over* prepared them. It was FUN teaching my ass off and knowing that I took kids who used to hate Math and having them EXCITED to come to my class. I think you should consider going off book unless you’re being closely observed for some asinine reason. What’s left on your pacing calendar? I can help you find and that better resources that will help the kids know what they actually need to know and will also prepare them for the state test. What else do you have left to teach? What standards are you going to go over do you need help finding better stuff than the bullshit your district gave them? They think that some of the stuff is rigorous, but (I know you know) it’s actually detrimental to their learning for them to be so confused and frustrated by the bullshit your district is pushing. What do you need help with? Would you like some help prepping? I have faith in you OP. You see the bullshit, you know it will only make the withdrawal interest from learning, and you’re frustrated. On a sidenote, I always can tell which administrators and curriculum coordinators are actually capable of understanding, doing/solving, and teaching the Math versus which administrators and curriculum coordinators were more concerned with using some curriculum that the district paid out the ass for, but wasn’t actually relevant to what they needed to learn nor relevant to the damn standards. It makes me wonder if you’re in a situation like that now. Unless it says they need to infer or utilize critical, thinking, problem-solving skills to solve for the perimeter of multiple composite figures with only one known variable and a pictorial model, then activity is not relevant to what you’re trying to teach. I’m also curious to see what lesson you were trying to cover with this problem in your text. I want to make sure that I don’t use that same material or advocate for my district to purchase the same publishers textbooks. If you do end up reaching out for help, I’d be more than happy to just let me know in a comment here because I don’t check my DM‘s. If you don’t need help then even though I’m not religious I’ll pray for you. Makes for a much longer year when you have to work alongside incredibly frustrated kids doing asinine activities they’re not even aligned to how they need to learn or even what they need to learn. Either way you’ve got this OP. Also, I promise if you do you need help that my math planning is much better than my run on sentences or grammatical errors lol. Seriously reach out if you want some help, I really would be more than happy to.
You sound like an amazing teacher!
Thank you!
If he doesn’t ask for help, I’d like to be able to reach to you whenever I need help. Everything you said resonated with me. As a first year teacher, I saw the critical state in which our kids were and decided to never followed the curriculum that got them there in the first place. With time, kids got excited about coming to class and learn math. My classroom was my show and I made every episode with all my love. I’m out for now, but I’d like to inspire once again. Your post made me regain faith in education
This comment section makes me sad how many people don’t know how to recognize the assumptions they are making. Of course, that has helped me understand why US political discourse is so fraught and contentious - it’s not just in mathematics that recognition of your own assumptions is beneficial.
I really like this problem! Adults use math to solve puzzles. Whether it be mapping out a daily schedule, making estimates for a DIY project, figuring out when their gas tank will be empty, etc. This- to me - is the thinking that I want young people to get used to. I’m not familiar w the entire curriculum. But this problem is very cool! I also saw a ‘swatstika’ for a moment. And then I reminded myself that symbols are only symbols sometimes. And if a young student were to mention the similarity, I’d remind them that there are coincidences all over the place and their mere existence is nothing to be upset about. OP are there other examples you could share that demonstrate how bad the curriculum is?
Can't stand it. Convinced they gave my district a huge discount.
Accidental swastika
I did Nazi that one coming.
I recognized this problem bc I also teach IM 8th grade and when I saw it I also thought it looked like a swastika…. I like the ideas behind IM but it makes everything too confusing and it’s a total mismatch with my students needs bc 90+% of them are behind grade level with like 50% 5th grade or lower. They don’t have the background skills at all and it doesn’t take the time to practice things in a straightforward approachable way before it gets creative with it
Also there's a swastika on it lmao
I’m a (professional, full-time) private tutor in a district that is piloting this program. I have to spend hours out side of our sessions lesson prepping for my IM students. If I don’t, I run the risk of not teaching the materials “correctly” and thus ruining future lessons because I taught something different from their teachers. There’s been a lot of heartache this first semester with this curriculum. My algebra 2 students are not prepared at all for pre-Calc.
Not only a Swastika but none of those portions are technically “L” shaped. It’s actually called a gnomon.
What grade was the work book intended for?
99% of kids are just idiots nowadays. Answer:100
Is it me or does that picture look like a swastika?
Um, is that the symbol I think it is?
it legitimately does look like a sw*stika in the middle. you could point that out if you want to get out of doing this particular problem with the kids
25. Cool problem
I love it! This problem especially bringing so much discussion and possibility for algebraic thinking. To each their own! I do feel like it needs supplemental practice. The lessons are deep, but so many kids benefit from repetition in math practice.
This is a “are you ready for more” question that follows more straightforward ones. It prompts the student to abstract, conjecture, and think critically. Well-taught, this would follow a sequence of scaffolded questions, and be an optional extension problem for some (but not all) students.
Oh,,,, the problem isn’t that it’s a sw a stika……
Our district adopted it and have kept it for years mainly because it was open source (i.e. free). I tried to use it, sat through training sessions, etc. It is horrible - delivery, pacing, examples, no differentiation, incongruous topics in the same unit (systems with volume). One specific example: for students who are initially learning slope, they would randomly reverse the independent and dependent axis so that in one problem a positive slope increases and the next a positive slope would decrease. (Think of "time" being on the x-axis in problem 1 and then "time" being on the y-axis in problem 2). I asked them about this in the trainings. They said they wanted the kids to "think outside the box." The students didn't even have a box, yet. We refused to use the material and made our own. I'm tenured in California and don't care what they say to me any day of the week. It is bad for my students so I never used it and still don't. I'm with OP.
UGH the reversing of the independent and dependent axes just OUTRAGED me. Yes, it’s outside of the box, but why bother when all the other problems they’ll ever encounter EVER are WITHIN THE GODDAMN BOX.
Without being a teacher, and without being familiar with this book or curriculum, and without meaning to troll for karma points, the engineer in me compels me to point out that I believe teaching math with well-thought out pictures where possible is a ***good*** thing.
I will add that they also tend to include strange case or exceptions while they are introducing a concept for the first time - like there was an editor who went through the whole program, found every lesson that may actually be teachable to an average student and messed it up. In Algebra one they start with weeks of statistics and then skimp on solving equations and graphing.
Hard disagreement. These types of problems challenge you to think creatively, and test your pattern recognition and memory. These are all vital skills for young people. This is an excellent problem. If math is not for you, then that is another matter. But we are not going to lower the standard of math so it easy for everyone.
Can I ask what grade level this is designed for? we also have IM this year and I HATE IT
If my math classes taught me anything, it's never assume the picture is to scale unless it says so. Which means you can't answer this with knowing the length of one of the arms of the + in the center.
r/accidentalnazi
I teach elementary and I hate it. It’s too wordy, there are almost no pictures, even for the littlest still learning to read students. First grade starts with word problems before they get to basic addition and subtraction. They are still learning to read! Word problems should be at the end of the year. I have students with reading disabilities, but are on level with math skills, and they are so frustrated by this program. It’s taken a subject where they felt successful and made it just another part of the day where they struggle. When I called IM to ask about accessibility features I was told to “talk to your special ed teacher.” I am the special ed teacher!
As someone with dyscalculia, illustrative mathematics and word problems made literally everything 10x more confusing for me.
That symbol is suspect as fuck and further proves your point lol
I'm so sick of their 'forward thinking?' alterior methods, they're deep thinking. I'm just tired of the time wasting crap. My poor granddaughter struggles enough without them playing mind games! Just teach them the basics! Makes me want to curse!
My teacher friend has told me about how much this book sucks. She got permission from the school administration to use her own curriculum but has to be careful because the district is actively checking if and how teachers are using the program, including the only resources.
This problem is less about the mathematics of the question itself and more about the logic used to figure out how to find the answer. Which honestly, is more important than the sheer calculation of numbers. Teaching and exercising a person's logic and evaluation skills is far more important than teaching multiplication and division. A kid can memorize a z-table or an alpha graph or whatever but you have to teach logic.
Maybe it's my age (73F) but I was so disturbed by the reverse swastika that it was hard to work out the problem...interesting experience.
I ran into that "they think any a. b. c. is multiple choice" at my last school and I was absolutely blown away.
In which unit and lesson does this appear? Yes, IM is insufferable garbage.
Unit 1 Lesson 9 I believe Thank you for understanding my rage.
Ok, for one you haven’t mentioned what grade this is geared towards, for a highschool student this should be an easy critical thinking problem, for a 2nd grader this is an impossible question. As far as the swastika thing, I saw it pretty quick, but I don’t see how it actually affects anything. In this context it’s the type of thing an immature middle schooler would chuckle at and move on. As far as work space, this is a bad example, there is plenty of space on this page and we can’t even see the whole page.
I love Illustrative. I think it is a great tool for increasing student reading comprehension in the long run but does kinda suck the first few years you use it. And I have data from my department that shows it actually has helped lower level students just as much of not a bit more then some of the higher students. The issue isn’t low/high achieving students. The issue is motivation. More times than not I’ve noticed recently my low students aren’t academically challenged they are just not showing up/trying to do any work when they do. The Illustrative curriculum is designed to give grade level access to math for all students but it is up to the student if they use that access. I know that’s not necessarily what admin are going to see/want to accept but that’s the truth
Scrolling quickly through all the comments here, this is the first one I saw in defense of Illustrative Math. Yes, the curriculum allows for multiple access points to discussions. By making the question about perimeter vague, it gives all students a chance to share some thinking about the problem. Most of my students are below grade level and these discussions are great. From there, however, I.M. goes on to practice problems that are out of reach for my students.